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The image shows a mathematical problem in Malay, asking about the quadratic function \( f(x) = -x^2 + 6x - 5 \). A straight line AB is parallel to the x-axis. We are required to determine the following:

### (a) Koordinat titik A (Coordinates of point A)
Since point A is on the x-axis, the y-coordinate will be 0. To find the x-coordinate of A, we solve \( f(x) = 0 \).

\[
f(x) = -x^2 + 6x - 5 = 0
\]

Solve this quadratic equation using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = -1 \), \( b = 6 \), and \( c = -5 \). Substituting these values:

\[
x = \frac{-6 \pm \sqrt{6^2 - 4(-1)(-5)}}{2(-1)} = \frac{-6 \pm \sqrt{36 - 20}}{-2} = \frac{-6 \pm \sqrt{16}}{-2} = \frac{-6 \pm 4}{-2}
\]

Thus,

\[
x = \frac{-6 + 4}{-2} = 1 \quad \text{or} \quad x = \frac{-6 - 4}{-2} = 5
\]

So, point A is at \( (1, 0) \).

### (b) Persamaan paksi simetri (Equation of the axis of symmetry)
The axis of symmetry for a quadratic function \( f(x) = ax^2 + bx + c \) is given by:

\[
x = \frac{-b}{2a}
\]

Substitute \( a = -1 \) and \( b = 6 \):

\[
x = \frac{-6}{2(-1)} = 3
\]

Thus, the axis of symmetry is \( x = 3 \).

### (c) Koordinat titik B (Coordinates of point B)
Since point B is on the same horizontal line (parallel to the x-axis) as point A, and both points share the same y-coordinate, we know \( B = (5, 0) \).

### (d) Koordinat titik maksimum P (Coordinates of the maximum point P)
The maximum point (vertex) of the parabola is located at the axis of symmetry, \( x = 3 \). To find the y-coordinate, substitute \( x = 3 \) into the function \( f(x) \):

\[
f(3) = -(3)^2 + 6(3) - 5 = -9 + 18 - 5 = 4
\]

Thus, the maximum point is \( P = (3, 4) \).

### Summary of Answers:
- (a) Koordinat titik A: \( (1, 0) \)
- (b) Persamaan paksi simetri: \( x = 3 \)
- (c) Koordinat titik B: \( (5, 0) \)
- (d) Koordinat titik maksimum P: \( (3, 4) \)

Would you like further details or have any questions?

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Here are 5 related questions to enhance your understanding:
1. How does the quadratic formula solve for roots of a quadratic equation?
2. What is the geometric meaning of the axis of symmetry for a quadratic graph?
3. Can you derive the vertex formula from completing the square method?
4. How do you determine if a parabola opens upwards or downwards?
5. Why do points A and B have the same y-coordinate if the line AB is parallel to the x-axis?

**Tip:** The vertex of a parabola is a critical point that helps determine the maximum or minimum value of a quadratic function.

Rajah di sebelah menunjukkan sebahagian daripada graf fungsi kuadratik f(x) = -x^2 + 6x - 5. Garis lurus AB adalah selari dengan paksi-x. Tentukan (a) koordinat titik A, (b) persamaan paksi simetri, (c) koordinat titik B, dan (d) koordinat titik maksimum P.

This problem explores the quadratic function f(x) = -x^2 + 6x - 5, requiring the determination of the coordinates of points A, B, and the maximum point P, along with the equation of the axis of symmetry. The solution uses the quadratic formula and axis of symmetry equation, suitable for high school students in Grades 10-12.

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